For each rational number not less than 2, we provide an explicit family of continued fractions of algebraic power series in finite characteristic (together with the algebraic equations they satisfy) which has that rational number as its diophantine approximation exponent. We also provide some non-qu
Continued fractions for certain algebraic power series
โ Scribed by W.H Mills; David P Robbins
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 822 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0022-314X
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๐ SIMILAR VOLUMES
We consider the continued fraction expansion of certain algebraic formal power series when the base field is finite. We are concerned with the property of the sequence of partial quotients being bounded or unbounded. We formalize the approach introduced by Baum and Sweet (1976), which applies to the
A recent paper (J. Number Theory 42 (1992), 61 87) announced various arithmetical properties of the Mahler function f (%, ,; x, y)= k=1 1 m k%+, x k y m . Unfortunately the arguments of that paper are marred by an error whereby the arguments hold only for ,=0 (or when b n =1 for all positive integer
Some time ago Mills and Robbins (1986, J. Number Theory 23, No. 3, 388-404) conjectured a simple closed form for the continued fraction expansion of the power series solution \(f=a_{1} x^{-1}+a_{2} x^{-2}+\cdots\) to the equation \(f^{4}+f^{2}-x f+1=0\) when the base field is GF(3). In this paper we